X-ray radiography and tomography are important methods for a variety of applications, for example non-destructive investigation of bulk samples, quality inspection of industrial products and non-invasive examination of anatomical structures and tissue regions of interest in the interior of a patient's body.
X-ray imaging based on attenuation of X-rays may yield excellent results where highly absorbing anatomical structures such as bones are embedded in a tissue of relatively weakly absorbing material. This is due to the fact that the penetration depth of hard X-ray beams may be rather high, which allows for recording sharp projections of the attenuation coefficient.
When different kinds of tissue with similar absorption cross-sections are under examination (for example in mammography or angiography), the contrast of X-ray absorption may be relatively poor. In this case, phase contrast X-ray radiography and tomography may be employed, where the change of phase of the X-rays penetrating the object of interest is examined. One method to obtain phase contrast information is the so-call differential phase contrast imaging as described in the following.
In differential phase contrast X-ray radiography and tomography, phase wrapping may occur. If the gradient of the phase front is outside the range of [−π; π] per grating period, the gradient is wrapped into this interval. This situation may appear in particular at the rim of an object, for example because of a big jump of the refractive index between air and tissue. The phase wrapping may happen for reasonable grating pitches of 2 μm for the phase grid already for object sizes below 1 mm. In particular in differential phase contrast X-ray tomography, this may lead to a strong capping artifact in the reconstructed image.